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Figure from:Symmetry in Architecture: Toward an Overdue Reassessment

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Figure 4: Common forms of symmetry in the natural world (top), and in human architectures (bottom). From left to right: reflectional (tiger and classical fagade with columns), rotational (sun during eclipse and stained- glass roof), translational (duck family and Islamic brick-and-tile wall), and scaling (fern leaf and Islamic Mugarnas pattern). Image credits: Top row, left: S Taheri via Wikimedia Commons; centre left: public domain (via Pixabay); centre right, public domain (via Maxpixel); right, public domain (via Free Nature Stock). Bottom row, left: Ryan Kaldari via Wikimedia Commons; centre left, Thomas Ledi via Wikimedia Commons; centre right, public domain (via Pixabay); right, public domain (via Pixabay).

Figure 4 Common forms of symmetry in the natural world (top), and in human architectures (bottom). From left to right: reflectional (tiger and classical fagade with columns), rotational (sun during eclipse and stained- glass roof), translational (duck family and Islamic brick-and-tile wall), and scaling (fern leaf and Islamic Mugarnas pattern). Image credits: Top row, left: S Taheri via Wikimedia Commons; centre left: public domain (via Pixabay); centre right, public domain (via Maxpixel); right, public domain (via Free Nature Stock). Bottom row, left: Ryan Kaldari via Wikimedia Commons; centre left, Thomas Ledi via Wikimedia Commons; centre right, public domain (via Pixabay); right, public domain (via Pixabay).

Related Figures (8)

Google Books Ngram Viewer Figure 1: Frequency of the term “symmetry” in books since 1800, according to Google Books Ngram Viewer (Google, 2021a).
Google Books Ngram Viewer Figure 1: Frequency of the term “symmetry” in books since 1800, according to Google Books Ngram Viewer (Google, 2021a).
Figure 2: Frequency of the term “architectural symmetry” in books since 1800, according to Google Books Ngram Viewer (Google, 202 1b). para. 15). In that document, the term “function” appears no less than 37 times.
Figure 2: Frequency of the term “architectural symmetry” in books since 1800, according to Google Books Ngram Viewer (Google, 202 1b). para. 15). In that document, the term “function” appears no less than 37 times.
Figure 3: Frequency of the term “architectural functionalism” in books since 1800, according to Google Books Ngram Viewer (Google, 2021c).
Figure 3: Frequency of the term “architectural functionalism” in books since 1800, according to Google Books Ngram Viewer (Google, 2021c).
Figure 5: Examples of buildings from before 1900 that exhibited many forms of symmetry, including reflectional, rotational, translational, scaling, and compound forms. Left, Santa Caterina del Sasso Monastery, Lake Maggiore, Italy; Center, Central Market, Valencia, Spain; right, Taktsang Monastery in Bhutan. Image credits: left, public domain (via Pixabay); center, @nosoylasonia via Photohere; right, Douglas J. McLaughlin via Wikimedia Commons. By “linking and mutual relationship” one might think of modern systems theory or group theory, and moreover tied to even more recent findings in neuroscience about aesthetic perceptions, about which more will be said below. What can be noted for the moment is that the forms of symmetry in buildings prior to 1900 were remarkably complex, and went far beyond simple reflectional or “mirror” symmetries.
Figure 5: Examples of buildings from before 1900 that exhibited many forms of symmetry, including reflectional, rotational, translational, scaling, and compound forms. Left, Santa Caterina del Sasso Monastery, Lake Maggiore, Italy; Center, Central Market, Valencia, Spain; right, Taktsang Monastery in Bhutan. Image credits: left, public domain (via Pixabay); center, @nosoylasonia via Photohere; right, Douglas J. McLaughlin via Wikimedia Commons. By “linking and mutual relationship” one might think of modern systems theory or group theory, and moreover tied to even more recent findings in neuroscience about aesthetic perceptions, about which more will be said below. What can be noted for the moment is that the forms of symmetry in buildings prior to 1900 were remarkably complex, and went far beyond simple reflectional or “mirror” symmetries.
Google Books Ngram Viewer Figure 6: Google Books Ngram Viewer of four of the most influential architects of the 20" century, Le Corbusier, Walter Gropius, Ludwig Mies van der Rohe and Frank Lloyd Wright (Google, 2021d).
Google Books Ngram Viewer Figure 6: Google Books Ngram Viewer of four of the most influential architects of the 20" century, Le Corbusier, Walter Gropius, Ludwig Mies van der Rohe and Frank Lloyd Wright (Google, 2021d).
Figure 7: Le Corbusier’s “functionalism” seems purely metaphoric when applying the towering forms of grain elevators, or the portholes and pipe railings of cruise ships (Le Corbusier, 1923).
Figure 7: Le Corbusier’s “functionalism” seems purely metaphoric when applying the towering forms of grain elevators, or the portholes and pipe railings of cruise ships (Le Corbusier, 1923).
Figure 8: The “glide reflection,” a form of compound symmetry, generates many rich tiling and interlocking patterns, including those of the Alhambra (bottom centre) and Westminster Abbey (bottom right). Images: Top left, Kelvinsong via Wikimedia Commons; top right, Martin von Gagern via Wikimedia Commons. Bottom left, Mathemalchemy group & Susan Goldstein; others in public domain.
Figure 8: The “glide reflection,” a form of compound symmetry, generates many rich tiling and interlocking patterns, including those of the Alhambra (bottom centre) and Westminster Abbey (bottom right). Images: Top left, Kelvinsong via Wikimedia Commons; top right, Martin von Gagern via Wikimedia Commons. Bottom left, Mathemalchemy group & Susan Goldstein; others in public domain.